Derangements of 1 2 3 4:
2 1 4 3 
2 3 4 1 
2 4 1 3 
3 1 4 2 
3 4 1 2 
3 4 2 1 
4 1 2 3 
4 3 1 2 
4 3 2 1 

Number of derangements:
    n         counted      calculated 
---------------------------------------
    0               1               1 
    1               0               0 
    2               1               1 
    3               2               2 
    4               9               9 
    5              44              44 
    6             265             265 
    7            1854            1854 
    8           14833           14833 
    9          133496          133496 

!20 = 895014631192902121